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What is the Objectivist explanation of how we know modus ponens?

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3 hours ago, EC said:

It's adding pure rationalism to subject matter that is naturally anti-rationalistic

I'm reading your post, but all I'm hearing is "symbolic notation! I don't understand, therefore rationalism".

It's a kind of animosity towards what is difficult to understand - after all, it looks like just playing with words and letters, so how could it possibly be meaningful? But if you slow down a little bit, it's like responding to any argument. Some are wrong, some are right, and some don't make sense. Some people actually like looking at symbols, others don't. Personally, I often prefer dealing with strictly words, but once in a while I actually enjoy dealing with symbolic notations. I especially like symbolic notations when I'm developing new ideas. It is an extremely intellectualized way of dealing with ideas, but it helps for simplification towards essential ideas. Not always so useful when talking about ethics, but very useful for epistemological topics like concept formation (which Rand considered to be very mathematical anyway). 

3 hours ago, EC said:

If something can't be stated in plain English it's unlikely to be true.

That means you've only dealt with extremely simplified ideas, or dealing with ideas passed down to you. This is even more like rationalism - dogmatic. How do we know modus ponens? It's complicated. But I know you've dealt with some advanced physics, so surely you can appreciate the complexities of what initially seems very simple. 

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On 4/6/2019 at 5:45 PM, William O said:

Modus ponens is, of course, the following pattern of inference:

  1. If p, then q.
  2. p.
  3. Therefore, q.

What is the Objectivist position on how we come to know this inference rule?

"The Objectivist position" here can mean either the position taken by Rand or the position taken by an Objectivist intellectual. I am pretty sure Rand never addressed this in the official Objectivist literature.

Thanks in advance.

From Rand: Axiomatic concepts are self evident.  

From Aristotle:  He gives us formal logic in the form of propositions, based on a principle of noncontradiction which can be named without relying upon a double negative as a "law of identity".

Back to Rand: Identity is an axiomatic concept.

Conclusion:  Logic is not self evident, but is derived from the self evident.  That modus ponens is a valid inference in logic is not work that Objectivism needs to duplicate.

Now I'm curious as to what end this question serves?  What did you really want to know?

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8 hours ago, Grames said:

From Rand: Axiomatic concepts are self evident.  

From Aristotle:  He gives us formal logic in the form of propositions, based on a principle of noncontradiction which can be named without relying upon a double negative as a "law of identity".

Back to Rand: Identity is an axiomatic concept.

Conclusion:  Logic is not self evident, but is derived from the self evident.  That modus ponens is a valid inference in logic is not work that Objectivism needs to duplicate.

I don't see how modus ponens is justified here, since you haven't mentioned modus ponens at all.

If you're saying that Aristotle's work contains a justification of modus ponens, my understanding is that he thought the categorical syllogism (e.g. Barbara: "All As are B, and all Bs are Cs, therefore all As are Cs") was the only form of logical inference. So I'd be very surprised to find out that he justified modus ponens.

Quote

Now I'm curious as to what end this question serves?  What did you really want to know?

Before I started this thread, I was very unclear about the epistemology of logic. That is, I was not sure how we arrive at the knowledge that the forms of inference are true using only observation and induction. Presumably this isn't just stupidity on my part, since virtually nobody outside of Objectivism would say it's possible to get logic from observation and induction.

This has been partially ameliorated by MisterSwig's short derivation of modus ponens from the law of identity. I am still not happy with the particular way he defends the law of identity, but that's a different topic really, and there can be no doubt of the law of identity itself.

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3 hours ago, William O said:

If you're saying that Aristotle's work contains a justification of modus ponens,

Aristotle was the fountainhead so to speak of a horde of later scholars working out everything implied by Aristotle's method, who can be collectively referenced as Aristotelians.  Some medieval working in Latin came up with  modus ponens. But just as in a valid syllogism the truth of the conclusion is contained within the premises, the formal validity of the various derivative forms of inference is contained within the method Aristotle first taught. 

The only important question is how Aristotle's reliance on non-contradiction is justified.  That is where Rand's notion of axiomatic concepts and propositions formed from them into axioms enters.

 

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4 hours ago, William O said:

Before I started this thread, I was very unclear about the epistemology of logic. That is, I was not sure how we arrive at the knowledge that the forms of inference are true using only observation and induction. Presumably this isn't just stupidity on my part, since virtually nobody  outside of Objectivism would say it's possible to get logic from observation and induction.

I must confess I'm confused about what you're asking. Are you asking how modus ponens is justified, how modus ponens was discovered ("how we come to know?"), how logic in general was discovered (specifically in terms of induction), or how necessity commits us to a conclusion, or how does the law of identity apply to modus ponens specifically? These are all different questions, though interrelated of course.

I'm reading here you're asking about how to "get logic" from induction. I'm not sure what this has to do with "Objectivism would say," what work did Rand do on logic theory? Simply saying "law of identity" doesn't begin to address the question. Nobody outside of Objectivism? I don't even know how to conceptualize what you're saying because presumably Rand didn't discover logic in the first place?

You might want to take a look at the primary texts like the Prior Analytics and the Topics in which Aristotle is formulating the ideas of "scientific demonstration" (as versus dialectic) and try to see what his method is. Obviously he doesn't just look out and go "law of identity" and somehow induce all these rules. You can see there is some "principal data" that he starts off with, like (a) that we are not imbued with automatic knowledge, and that (b) we have made mistakes before, and yet (c) we have also been right and had certainty before. He then moves to pointing out that experience has brought mankind into contact with various cases of making judgments and being right and being in error. He also undoubtedly was familiar with the texts of Euclid and geometers and utilized their methods (and makes reference that he is borrowing some of their terminology and many of his examples are mathematical.) The analyst (logician) then assembles various arguments and analyzes their terms and propositions to try and sort through what causes different ones to be erroneous or certain. We can then see that there is a certain form (or structure) common to all the valid forms of demonstration. Thus he arrives at the PNC and excluded middle in Posterior Analytics I.11-12 and in more detail in Metaphysics 6. Notice it is not until after we have already been using and have been shown to have logical knowledge and have already presupposed its first principles, before we arrive at what those rules and foundational axioms are. Also we cannot demonstrate deductively a proof of the first principles of inference because they would then be derived from something else that is more first (71b20-72a) and nothing can be demonstrated except from its own principles, therefore the first principles must be immediate (76a38-b2.)

Of course later logicians like Theophrastus and Galen used Aristotle as a reference to notice more connections and categories than he did (like "what if we posit certain conditionals, if I'm committed to this belief, and this belief entails that belief, then I'm also committed to that one," ie., modus ponens.) But by not putting this "principal data" or "starting point" out of mind, we can see the inductive method at work in the discovery of logic.

Edited by 2046

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The Stoics were the first to develop an explicit theory of propositional connectives. An example they used of what now we call modus ponens: If it is day, then it is light. It is day. Therefore, it is light.

The basic unit of Stoic logic is not the term, as in Aristotle, but the proposition.

Modus ponens is a form of valid argument that students in a first logic course say Yes to right off. They see its validity, and it’s as if one had already known it was a valid form of reasoning before seeing it in the course. Not so with material implication, which is a more contrived creature of modern logic.

William O,  John Stuart Mills is the one most famous for giving an empiricist answer to how we come to know logical principles such as modus ponens. The logical empiricists (also called logical positivists) thought such principles are somehow gotten from experience, though it could not be gotten as Mills proposed. Aristotle and Rand/Peikoff also suppose learning of basic logical principles must come from experience (in the present life of an individual), but not in the empiricist way of Mills or in the experiential ways we learn unsupported bodies fall or learn that we have receptors in the skin that guage coolness or warmth by rate and direction of heat transfer.

I do not think that questions of origins of any of the various sorts of knowledge that individuals attain, from infancy to a first course in geometry, can be answered in the finest way without assimilation of the pertinent results of cognitive developmental psychology of the last 70 years.

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I think the thing really missing here is the specific discussion on concepts of consciousness. Swig seemed to imply that for such concepts to exist is Kantian and is some kind of attack on Oist epistemology - when in fact it is something that Rand spoke about very briefly. Actually, I'm not even satisfied with her answer about how we form concepts referring to our inner mental life. Should we reject internalism (that at least some non-perceptual information can count as evidence) completely, in favor of a purely externalized (external, is in outside our selves) account of concepts? I don't think so. 

Any rule of logic or logical operator itself can be formed as a concept through introspection alone, because they would refer to the ways that propositions and concepts can be manipulated. Propositions and concepts exist only as mental existents. Although we can trace this down to perception, the material we are working with is all mental content. We can stick to internal evidence; we don't perceive free will, we don't perceive emotions, yet these things count as valid evidence. The content of consciousness is not perception. 

But how do we take the step to then say that any concept of consciousness is connected to reality? Repeated observation of applying concepts of consciousness is just an empiricist error, because there's only statistical regularity (association). 

I wouldn't want to treat modus ponens as a consequence or result of continued reasoning from beginning with entities. Not to say that it must be detached from reality, I mean that these kinds of concepts are formed very differently and begin with introspection. 

1 hour ago, Boydstun said:

I do not think that questions of origins of any of the various sorts of knowledge that individuals attain, from infancy to a first course in geometry, can be answered in the finest way without assimilation of the pertinent results of cognitive developmental psychology of the last 70 years.

This is the right kind of approach, and why I think even type theory in math is beneficial. I think philosophizing with specialized knowledge folded in is necessary to figure out answers. (Keep in mind the spiral theory of knowledge: even though any specialized knowledge is dependent on philosophy, we can bring in specialized knowledge formed later as ways to further understand something you already formed a concept about. )

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Well I mean I agree logic is not learned through some sort of transcendental argument (X is a necessary condition for Y, Y therefore X), although Aristotle does deploy something like that in his "negative demonstration," but he is also careful to say this isn't the same thing as a proof of the PNC. 

And yes you're going to need some story about how we form any beliefs whatsoever, because when we're talking about logical propositions, we're talking about reasons for believing things. You also need a theory of semantic reference, and of course all the rest of epistemology as well.

But I do think you have to start by beginning with entities. I think, for modus ponens, the introspection comes when you are positing "If I held this belief..." The sort of fact "I have this belief" is internal, but intensional in the sense that it is about something. Someone asked the function of "if." In English the word "if" is etymologically related to "to give" in the sense of "let me grant..." or "let me suppose..."

If it is Friday, then 2046 will be wearing jeans.

It is Friday.

Therefore 2046 will be wearing jeans.

If Eiuol believed the premises, it would be immediately something he could "say Yes" to in Boydston's sense, because he is seeing the internal connections between his own beliefs. He'd see his own beliefs gave him a reason to believe the conclusion. Thus if Eiuol later on were to think about "why is that a valid form of inference?" he'd be thinking about his own internal belief structure in a sense. And it would be inductive in the sense that he'd already have to know modus ponens and be using modus ponens and then think about an instance of himself using it.

Yes he'd need a theory about why did he form the belief about 2046 wearing jeans in the first place, and he'd need a theory about how "jeans" refers to those things I'm wearing, and so on. I mean technically he'd need a quantum physics theory about how the particles are doing things in his head.

There are multiple levels of explanation to any given thing. If a kid asked you "why does the square block not fit into the round hole?" and you said "Well, see look, the blocks are made of wood, and it has these particles bonded together made of various molecules and then surfaces collide and there's friction and resistance, and really there's these atoms with various charges whirling around in orbits," etc., Technically you wouldn't be giving a wrong explanation, but is it a better one than "because it's shaped that way"? It seems like we are all looking to different levels of analysis here. Perhaps Aristotle's four causes are a better concept of causality, but I think the simplest explanation is "because you already committed yourself to believing one thing, and you see that thing is related to another."

 

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1 hour ago, 2046 said:

Well I mean I agree logic is not learned through some sort of transcendental argument (X is a necessary condition for Y, Y therefore X), although Aristotle does deploy something like that in his "negative demonstration," but he is also careful to say this isn't the same thing as a proof of the PNC. 

And yes you're going to need some story about how we form any beliefs whatsoever, because when we're talking about logical propositions, we're talking about reasons for believing things. You also need a theory of semantic reference, and of course all the rest of epistemology as well.

But I do think you have to start by beginning with entities. I think, for modus ponens, the introspection comes when you are positing "If I held this belief..." The sort of fact "I have this belief" is internal, but intensional in the sense that it is about something. Someone asked the function of "if." In English the word "if" is etymologically related to "to give" in the sense of "let me grant..." or "let me suppose..."

If it is Friday, then 2046 will be wearing jeans.

It is Friday.

Therefore 2046 will be wearing jeans.

If Eiuol believed the premises, it would be immediately something he could "say Yes" to in Boydston's sense, because he is seeing the internal connections between his own beliefs. He'd see his own beliefs gave him a reason to believe the conclusion. Thus if Eiuol later on were to think about "why is that a valid form of inference?" he'd be thinking about his own internal belief structure in a sense. And it would be inductive in the sense that he'd already have to know modus ponens and be using modus ponens and then think about an instance of himself using it.

Yes he'd need a theory about why did he form the belief about 2046 wearing jeans in the first place, and he'd need a theory about how "jeans" refers to those things I'm wearing, and so on. I mean technically he'd need a quantum physics theory about how the particles are doing things in his head.

There are multiple levels of explanation to any given thing. If a kid asked you "why does the square block not fit into the round hole?" and you said "Well, see look, the blocks are made of wood, and it has these particles bonded together made of various molecules and then surfaces collide and there's friction and resistance, and really there's these atoms with various charges whirling around in orbits," etc., Technically you wouldn't be giving a wrong explanation, but is it a better one than "because it's shaped that way"? It seems like we are all looking to different levels of analysis here. Perhaps Aristotle's four causes are a better concept of causality, but I think the simplest explanation is "because you already committed yourself to believing one thing, and you see that thing is related to another."

 

I would like to say I like what you said but something about it makes me uneasy.

I’m sorry if I haven’t followed perfectly, but with respect to your statements about Friday, 2046, and jeans, you seem to be characterizing those statements as if their  referents were mental contents or beliefs, i.e. that’s what those statements are “really” about, whereas when I read them they seem quite straightforwardly and explicitly to refer to reality... specifically, Friday, 2046, and jeans.

“IF” something in reality IS, what I grant or take for granted or suppose is beside the point... no?

 

Edited by StrictlyLogical

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2 hours ago, Eiuol said:

Any rule of logic or logical operator itself can be formed as a concept through introspection alone,

After having a decade or so of growing up in the real world and having that store of background information, then sure some introspection is possible relevant to learning entry level abstractions such acceleration or the logarithm.  But all that background information came from perception and lower level concepts.  That last word "alone" can be misleading.

 

2 hours ago, Eiuol said:

We can stick to internal evidence; we don't perceive free will, we don't perceive emotions, yet these things count as valid evidence. The content of consciousness is not perception. 

Emotions are perceptible as changes in body state.  If there is no body state change, you are not actually "feeling" or experiencing the emotion are you?  Volition is also experienced directly.  

Directing one's attention outward is extrospection, inward is introspection, and awareness of the middle ground that is the internals of one's own body is interoception.  There is no content of consciousness which is not derivative of extrospection or interoception, and by "derivative of" I am referencing Rand's epistemology of concepts of concepts.

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1 hour ago, StrictlyLogical said:

I would like to say I like what you said but something about it makes me uneasy.

I’m sorry if I haven’t followed perfectly, but with respect to your statements about Friday, 2046, and jeans, you seem to be characterizing those statements as if their  referents were mental contents or beliefs, i.e. that’s what those statements are “really” about, whereas when I read them they seem quite straightforwardly and explicitly to refer to reality... specifically, Friday, 2046, and jeans.

“IF” something in reality IS, what I grant or take for granted or suppose is beside the point... no?

 

If I understand you, of course it's important to distinguish somebody believing something from the something that they believe. Just because somebody believes something doesn't make the thing they believe true. The reason I went into all that, I said that when you give reasons for a belief, what you're doing is you’re giving reasons to believe that belief is true. Reasons are reasons for all of us because beliefs are about some being. Apprehension comes through beliefs, that doesn't mean apprehension is only of beliefs.

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8 hours ago, 2046 said:

If I understand you, of course it's important to distinguish somebody believing something from the something that they believe. Just because somebody believes something doesn't make the thing they believe true. The reason I went into all that, I said that when you give reasons for a belief, what you're doing is you’re giving reasons to believe that belief is true. Reasons are reasons for all of us because beliefs are about some being. Apprehension comes through beliefs, that doesn't mean apprehension is only of beliefs.

All well and good if we are dealing with apprehension ... i.e. if the statement’s referents are apprehension of things rather than things themselves. But that is the very thing I am questioning.

Of course statements don’t have to always be about Friday, 2046, and jeans (and clearly some statements can be solely about those kinds of things) different ones could specifically refer to apprehension in connection with those things, others could refer to belief about those things, others could refer to other statements about those things or the truth of other statements about those things, but we should be careful not to conflate the types of statements we are actually dealing with.

 

Statements about the process of thought are not the same as statements about reality used as part of a process of thought.

Edited by StrictlyLogical

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On 4/10/2019 at 6:13 AM, William O said:

...virtually nobody outside of Objectivism would say it's possible to get logic from observation and induction.

Can you clarify or reiterate what is meant by "get logic"? I'm wondering if you mean that man starts out without logic and then at some point acquires it. If so, what then is meant by "logic"? For, as Peikoff has argued, without logic man would be stuck at the perceptual level.

"[K]nowledge cannot be acquired by experience apart from logic, nor by logic apart from experience. Without the use of logic, man has no method of drawing conclusions from his perceptual data[.]" (The Analytic-Synthetic Dichotomy)

Logic is man's method, or form, of cognition. We use it to form our first concepts. It is only later that we identify it as such, recognize its basic law, and develop it into a system of rules.

Edited by MisterSwig

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On 4/6/2019 at 4:45 PM, William O said:

Modus ponens is, of course, the following pattern of inference:

  1. If p, then q.
  2. p.
  3. Therefore, q.

What is the Objectivist position on how we come to know this inference rule?

"The Objectivist position" here can mean either the position taken by Rand or the position taken by an Objectivist intellectual. I am pretty sure Rand never addressed this in the official Objectivist literature.

Thanks in advance.

In general, we know patterns of inference as codifications of regularly successful mental policies. In particular, we know logically valid inference patterns as means to certain conclusions, the denial of which results in contradiction. But seeing as conceptual knowledge and method are indivisible, valid forms of inference are less what we may know than that by which we know (conceptually). The knowing of logic and of basic inference patterns are in large part the faculty of knowledge turning back in on itself, and stating the implicit causal relations by which one knows as explicit propositional forms or rules for one to know.

Modus ponens is an explicit statement of the indivisibility of cause and effect, a principle implicit in every mental consequence as caused by the apprehension of some object of consciousness. "p therefore q" underscores the premise behind all valuation and recognition, for it is in recognizing the necessary connection between q and its cause that motivation may find real purchase.

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On 4/10/2019 at 10:46 AM, 2046 said:

I must confess I'm confused about what you're asking. Are you asking how modus ponens is justified, how modus ponens was discovered ("how we come to know?"), how logic in general was discovered (specifically in terms of induction), or how necessity commits us to a conclusion, or how does the law of identity apply to modus ponens specifically? These are all different questions, though interrelated of course.

I'm asking how modus ponens is justified. I am not (knowingly) asking about child psychology or the history of logic.

It is fair to ask of any item of knowledge "how do we know X?" The reason for this is that there is no such thing as innate knowledge or divine revelation, which means that all knowledge must be traceable by some series of steps back to observation (the given). So for example, "how do we know the earth is round?" and "how do we know concepts are formed by measurement omission?" are fair questions. I'm just substituting modus ponens for X in this formula.

Quote

I'm reading here you're asking about how to "get logic" from induction. I'm not sure what this has to do with "Objectivism would say," what work did Rand do on logic theory? Simply saying "law of identity" doesn't begin to address the question.

Yes, I made a mistake in the OP. What I tried to do if you look back is to stipulate that "the Objectivist answer" means either the answer given by Rand or the answer given by an Objectivist intellectual. This was a bad idea on my part and it has contributed to considerable confusion since it directly contradicts the correct definition of Objectivism as the philosophy of Ayn Rand.

Quote

Nobody outside of Objectivism? I don't even know how to conceptualize what you're saying because presumably Rand didn't discover logic in the first place?

Overwhelmingly, philosophers have maintained that logic and mathematics are not justified by observation and induction. That is what I meant, although naturally logic itself is much less controversial than philosophy of logic.

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40 minutes ago, William O said:

Overwhelmingly, philosophers have maintained that logic and mathematics are not justified by observation and induction. That is what I meant, although naturally logic itself is much less controversial than philosophy of logic.

Sure, modern philosophers approach logic from different views than the way Rand does. There are too many versions to anthologize here, more than one person can even know if he specializes in, probably. Perhaps there are two factors common to a lot of these approaches (a) a lack of confidence in induction in general, and (b) that logic is a purely formal system of variables and stipulated transformational rules that form a closed system quite apart from the question of whether these variables stand for anything. Accordingly when any group of symbols can be combined according to the stipulated rules of the system, then that is a valid expression of the system, if not then that is an invalid expression in that system. Different systems can then disagree about how, if at all, the relations between the different schemas and variables function.

But it's not that Rand has a sui generis view of the situation of logic, but rather that she holds the classical view that the function of logic is a practical instrument (an organon) of human thought for understanding things in terms of what they are and thus preserving the relationship of identity. Moreover the only way to arrive at generalized premises are through induction, including in discovering logic itself, by assembling successful and unsuccessful examples and sorting through their common forms. Aristotle, as I tried to show, does display an inductive method in his logical texts.

Rand can be thought of as pointing back to this "old fashioned" way of conceiving logic. Peikoff does speak of a "split between logic and experience" that modern thought effected. And his NBI lectures does seem to point to classical logical ontologism (which is what he did his dissertation on.) Rand in ITOE does speak to "concepts of method" very briefly (p. 36) in connection with logic as abstracting from the content of thought to the correct steps needed to complete an identification (at least that's how I interpret what she's saying there.)

The neo-Aristotelian philosopher Henry Veatch has a good book that I've used in discussions: Two Logics: The Conflict between Classical and Neo-Analytic Philosophy if you can find a copy.

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4 hours ago, 2046 said:

The neo-Aristotelian philosopher Henry Veatch has a good book that I've used in discussions: Two Logics: The Conflict between Classical and Neo-Analytic Philosophy if you can find a copy.

Can you give a couple points that make this a good book? I'm very interested in this topic. Thanks.

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On 4/12/2019 at 11:01 AM, 2046 said:

The neo-Aristotelian philosopher Henry Veatch has a good book that I've used in discussions: Two Logics: The Conflict between Classical and Neo-Analytic Philosophy if you can find a copy.

The linked page has a Libraries button. When I clicked it, the title wasn't auto-fed to the new page. However, entering the title and clicking Find a Library gives search results as a list of titles. Clicking on a title there may help in locating a copy of the book in a library not too far away.

A good review of the book is here.

 

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6 hours ago, merjet said:

A good review of the book is here.

Has Veatch stumbled upon the Stolen Concept Fallacy and applied it to every single concept of the relating-logician via his Inverted Intentionality Fallacy? Every concept would be stolen (inverted) because every concept has its roots in existence, yet the relating-logician denies knowledge of existence. If so, this is brilliant. Rand and the professors touch on this in ITOE on page 250, where they argue that Locke, Berkeley, Hume, and Descartes don't really have a concept of existence.

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On 4/7/2019 at 8:41 AM, 2046 said:

in classical logic [...] the conclusion "preserves" the truth of the premises

Ordinarily it is not said that a conclusion preserves truth, but rather that an inference rule does or does not preserve truth. An inference rule is truth preserving if and only if whenever the rule is applied to true premises it yields a true conclusion. Those inference rules that preserve truth are are said to be valid. Or, more generally, we may say that an argument is truth preserving (valid) if and only if the conclusion is a logical consequence of the premises.

Edited by GrandMinnow

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21 hours ago, MisterSwig said:

Has Veatch stumbled upon the Stolen Concept Fallacy and applied it to every single concept of the relating-logician via his Inverted Intentionality Fallacy?

Sorry. I can't answer that, since I haven't read Veatch's book. I have ordered it via inter-library loan.

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On 4/12/2019 at 10:01 AM, 2046 said:

Sure, modern philosophers approach logic from different views than the way Rand does. There are too many versions to anthologize here, more than one person can even know if he specializes in, probably. Perhaps there are two factors common to a lot of these approaches (a) a lack of confidence in induction in general, and (b) that logic is a purely formal system of variables and stipulated transformational rules that form a closed system quite apart from the question of whether these variables stand for anything. Accordingly when any group of symbols can be combined according to the stipulated rules of the system, then that is a valid expression of the system, if not then that is an invalid expression in that system. Different systems can then disagree about how, if at all, the relations between the different schemas and variables function.

Modern logic concerns itself with both syntax (which is purely formal) and semantics (meanings of the expressions). 

/

'valid' may mean different things in context (varying among different authors in modern logic). But usually, 'valid' does not refer merely to whether the expression is obtained according to the syntax rules (the expression is well formed), but rather to whether the expression is a formula that is true in all interpretations of the language. So the notion you are referring to is more usually known as 'well-formedness', while the notion of ''validity' refers to semantics.

Edited by GrandMinnow

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